So Win7 will run on SSD1 on th old machine and SSD2 on the new machine, yes? And you want to move HDD3 from old machine to new and run the games on it?
Unfortunately, the new installation of Windows won't know about the games on the D drive that it inherits. Any application that is "portable" will still run from the drive, but these are few and far between. Most depend on files put into the windows directory structure and entries in the registry to run. So the odds are that you would have to reinstall the games afresh on SSD2.
You might be able to run SSD1 in the new machine if you do a Repair installation followed by updates to update to the appropriate drivers for the new system. Technically, you would have to change the product key from the old one to the new one - activation might be an issue.
Personally, I usually welcome the chance to do a clean build, so I don't have experience transferring OSes from one machine to another.